This paper considers a theoretical model of n asymmetric firms that reduce their initial unit costs by spending on R&D activities. In accordance with Schumpeterian hypotheses we obtain that more efficient (bigger) firms spend more in R&D and this leads to a more concentrated market structure. We also find a positive relationship between innovation and market concentration. This calls for a corrective tax on R&D activities to curtail strategic incentives to over-invest in R&D trying to achieve a higher market share.